In Taharah Kehalocha (vol. 1 pg. 201), Rabbi Y. Farkash cites the Kitzur Shulchan Aruch (153:10) who forbids and the Pischei Teshuva (YD 195:10) and Igros Moshe (YD 2:75) who are in doubt about the matter but tend to be stringent. Accordingly, he rules that one should be stringent in the matter wherever a Kol Isha concern would arise with a non-relative1. The Minchas Yitzchok (7:70) additionally prohibits even musical instruments if she plays them for her husband's enjoyment.

However, there are those who disagree - claiming that listening to one's niddah wife singing cannot be compared to listening to other women. They claim that gazing at parts of a women's body that are usually uncovered is certainly worse than hearing her sing, and since this is permitted when his wife is niddah (Shulchan Aruch YD 195:7), it is certainly permitted to hear her sing (Suga Bashoshanim 195:2, and Mishnas Yaakov vol. 3 pg. 117 in the name of Chemdas Moshe (58)).

The Ben Ish Chai (Year 2, Parshas Tzav 25), after writing that the wife should not put the baby to sleep by singing to it when she is niddah if her husband can hear, writes that, "If the baby is crying alot and will not fall asleep any other way and there is nowhere for the husband to go - it seems that one could be lenient."

Based on the above, Rabbi Farkash concludes that although we should follow all those who are strict, in a time of difficulty where there is no other option one may be lenient.

1 His assessment of that includes his citing the Chok Yaakov (OC 479:6), Yosef Ometz (603) and Otzer Haposkim in the the name of other poskim who forbid listening to a woman singing Zemiros on Shabbos, as well as the Shevet Halevi (Shu"t 5:197:4 and Shiurim 6:2 "Vegam B'Zmiros") who applies such a prohibition even when there are other people singing along (see also Suga Bashoshanim 16:6-7 and Be'er Moshe there).

The Ben Ish Chai is actually writing for the husband וצריך ליזהר אם אשתו נדה, אך אם הילד בוכה הרבהנוצריך לזמר זה שמלומד בכך, ואין מקום לבעל לילך שם, נראה דיש להקל. As such this along with the other maareh mikomos does not answer the question posed concerning the wife. But you are in good company as seen in all the other answers.
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user6591Nov 30 '14 at 2:59

There seems to be a misunderstanding of the Shevet Halevi going on. In 5:197:4 he writes that multiple women singing together doesn't mitigate the issue of Kol Isha (it is clearly not discussing the case of one's wife). Later in the same piece he mentions that he thinks the issue of Kol Isha by one's Niddah wife is dependant on two opinions in the Perisha, with the Perisha ruling accd to the side that would indicate that it is permitted! (I accept that in the Shiurim he takes it as obvious that a prohibition of Kol Isha applies to one's Niddah wife.)
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Double AA♦Jan 25 at 0:47

Incidentally, the Shevet Halevi in the next responsum (198) rules that a woman's speaking voice is included in Kol Isha if it is designed to be friendly like saying "Hello" or extended at all in duration. Hence long conversations with one's wife or saying "Hi, how was your day?" are seemingly also prohibited.
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Double AA♦Jan 25 at 1:12